We've faced this dilemma ourselves a few times, since we removed an intrusive shower head and now only bathe (an additional flexible shower hose was added for rinsing). The honest answer is it all depends on determining factors such as water pressure, whether a low-flow shower head is being used, how large the tub is, how much it is normally filled to, and of course how long the person showers.

But we think in your specific case, you have some legs to stand on to claim you're the more efficient bather, since the average bath takes between 30-50 gallons of water (we now only fill it a tad over half way) and a normal shower uses 20 gallons every 4 minutes. Replace that regular shower head with a water miser low-flow and you can cut that figure in half. Do the math and you're doing okay compared to the mermaid known as your roommate in either case.

To determine actual water use, both of you can measure the height of the water for an average bath or shower (just plug up the drain for a shower). You might need to time one another without each other knowing so neither tries to shave off time knowing they're being measured, but hopefully both of you are honest enough to want to know the facts. But the real goal would be for both of you to use just a little less water each time you bath or shower, which seems easy enough during warmer weather anyhow.

On a related note, we heard an interesting statistic on CNN the other day which mentioned that on average, Southern California residents already use 25% less water than the rest of the nation. Now that's impressive, but admittedly not enough considering our water use [waiting for angry jeers from Northern Cali folks]. Hopefully more of us can willingly conserve before it becomes a necessity, even if it means a shorter shower or less filled bath.